The general strategy to compute charged matters coupling in \(E2\) 
instanton background has been outlined in [1]}. In our case,
\({}<(H_{u}H_{d})^{2}>_{E2-inst}&=&\int d^{4}x \sum _{conf}\prod _{a}(\prod _{i=1}^{4}d\lambda _{ai})\times (\prod _{j=1}^{4}d\bar{\lambda }_{aj})e^{-S_{inst}}e^{Z^{\prime }}\nonumber \\&\times &<H_{u}>_{\lambda _{a1},\bar{\lambda }_{a1}}<H_{d}>_{\lambda _{a2},\bar{\lambda }_{a2}}<H_{u}>_{\lambda _{a3},\bar{\lambda }_{a3}}<H_{d}>_{\lambda _{a4},\bar{\lambda }_{a4}}\) 
